منابع مشابه
Catalan structures and Catalan pairs
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced in [DFPR] with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan structure to the recursive definitio...
متن کاملCoincidences of Catalan and Q-catalan Numbers
Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday
متن کاملParametric Catalan Numbers and Catalan Triangles
Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schröder numbers and small Sch...
متن کاملCatalan numbers
Catalan numbers appear in many places throughout mathematics, and are a fairly frequent subject for articles in this magazine. Indeed, a very nice introduction to their properties was given in this magazine by Vun and Belcher [3], and a historical account of their discovery in Chinese mathematics (before Catalan!) has also appeared in a recent article by Larcombe [1]. The article by Vun and Bel...
متن کاملMultivariate Fuss-Catalan numbers
are integers that appear in many combinatorial problems. These numbers first arose in the work of Catalan as the number of triangulations of a polygon by mean of nonintersecting diagonals. Stanley [13, 14] maintains a dynamic list of exercises related to Catalan numbers, including (at this date) 127 combinatorial interpretations. Closely related to Catalan numbers are ballot numbers. Their name...
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ژورنال
عنوان ژورنال: ACM Transactions on Asian and Low-Resource Language Information Processing
سال: 2019
ISSN: 2375-4699,2375-4702
DOI: 10.1145/3312575